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Conditional Akaike information criterion in the Fay-Herriot model. (English) Zbl 1365.62017

Summary: The Fay-Herriot model, a popular approach in small area estimation, uses relevant covariates to improve the inference for quantities of interest in small sub-populations. The conditional Akaike information (AI) [F. Vaida and S. Blanchard, Biometrika 92, No. 2, 351–370 (2005; Zbl 1094.62077)] in linear mixed-effect models with i.i.d. errors can be extended to the Fay-Herriot model for measuring prediction performance. In this paper, we derive the unbiased conditional AIC (cAIC) for three popular approaches to fitting the Fay-Herriot model. The three cAIC have closed forms and are convenient to implement. We conduct a simulation study to demonstrate their accuracy in estimating the conditional AI and superior performance in model selection than the classic AIC. We also apply the cAIC in estimating county-level prevalence rates of obesity for working-age Hispanic females in California.

MSC:

62B10 Statistical aspects of information-theoretic topics
62D05 Sampling theory, sample surveys
62F10 Point estimation

Citations:

Zbl 1094.62077
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References:

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